Category Archives: mathematics

Gee, if all maths classes were like this, they’d be exhausting …

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Jeff wins the Adams Prize

My son, Jeff, is Professor of Mathematics, University College London. The Adams Prize is described here, and here on Wikipedia. It’s a Big Deal. To quote the description of it from the University of Cambridge: The Adams Prize is one … Continue reading

Posted in mathematics | 2 Comments

Humble Alternatives to Daylight Savings Time — Math with Bad Drawings

From the ever clever and entertaining Ben Orlin. And the drawings really aren’t bad.

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a song in praise of data scientist Rebekah Jones

I linked to Rebekah Jones‘ keynote address at the August 2020 Data Science Conference on COVID-19 sponsored by the National Institute for Statistical Science. Below is a song in tribute to her, wishing her well. (h/t Bill McKibben) We’re doing … Continue reading

Posted in American Association for the Advancement of Science, American Mathematical Society, American Statistical Association, Boston Ethical Society, children as political casualties, Data for Good, data science, geographic, geographic information systems, International Society for Bayesian Statistics, journalism, mathematics, New England Statistical Society, pandemic, Rebekah Jones, Risky Talk, science, Significance, statistical ecology, statistics, the problem of evil, whistleblowing, ``The tide is risin'/And so are we'' | Leave a comment

Complexity vs Simplicity in Geophysics

Originally posted on GeoEnergy Math:
In our book Mathematical GeoEnergy, several geophysical processes are modeled — from conventional tides to ENSO. Each model fits the data applying a concise physics-derived algorithm — the key being the algorithm’s conciseness but not…

Posted in abstraction, American Association for the Advancement of Science, American Meteorological Association, American Statistical Association, Azimuth Project, complex systems, control theory, differential equations, dynamical systems, eigenanalysis, information theoretic statistics, mathematics, Mathematics and Climate Research Network, mechanistic models, nonlinear systems, Paul Pukite, spectra, spectral methods, spectroscopy, theoretical physics, wave equations, WHT | Leave a comment

“We will love science and its controversies.”

We will continue, Professor. With all the teachers and professors in France, we will teach history, its glories and its vicissitudes. We will introduce literature, music, all works of soul and spirit. We will love with all our strength the … Continue reading

Posted in Charlie Hebdo, martyrs to truth, mathematics, religion, science | Tagged , | Leave a comment

We are all Mathematicians

Bobby Seagull. Great.

Posted in mathematics, mathematics education, maths | Leave a comment

Reanalysis of business visits from deployments of a mobile phone app

Updated, 20th October 2020 This reports a reanalysis of data from the deployment of a mobile phone app, as reported in: M. Yauck, L.-P. Rivest, G. Rothman, “Capture-recapture methods for data on the activation of applications on mobile phones“, Journal … Continue reading

Posted in Bayesian computational methods, biology, capture-mark-recapture, capture-recapture, Christian Robert, count data regression, cumulants, diffusion, diffusion processes, Ecological Society of America, ecology, epidemiology, experimental science, field research, Gibbs Sampling, Internet measurement, Jean-Michel Marin, linear regression, mark-recapture, mathematics, maximum likelihood, Monte Carlo Statistical Methods, multilist methods, multivariate statistics, non-mechanistic modeling, non-parametric statistics, numerics, open source scientific software, Pierre-Simon Laplace, population biology, population dynamics, quantitative biology, quantitative ecology, R, R statistical programming language, sampling, sampling algorithms, segmented package in R, statistical ecology, statistical models, statistical regression, statistical series, statistics, stepwise approximation, stochastic algorithms, surveys, V. M. R. Muggeo | 1 Comment

“The truly common core”

Repost of “The truly common core“, from Ben Orlin‘s Math with Bad Drawings blog.

Posted in education, mathematics, mathematics education, maths | Leave a comment

Cumulants and the Cornish-Fisher Expansion

“Consider the following.” (Bill Nye the Science Guy) There are random variables drawn from the same kind of probability distribution, but with different parameters for each. In this example, I’ll consider random variables , that is, each drawn from a … Continue reading

Posted in Calculus, closed-form expressions, Cornish-Fisher expansion, cumulants, descriptive statistics, mathematics, maths, multivariate statistics, statistical models, statistics, theoretical statistics | Leave a comment

Another reason why the future of Science and STEM education in the United States is cloudy

From Nature‘s “Universities spooked by Trump order tying free speech to grants“, with the subheading “White House policy will require universities to certify that they protect free speech to remain eligible for research funding”, comes this chilling news: US President … Continue reading

Posted in American Association for the Advancement of Science, American Mathematical Society, American Statistical Association, an ignorant American public, an uncaring American public, anti-intellectualism, anti-science, climate change, Commonwealth of Massachusetts, emigration, European Union, mathematics, science, United States | Leave a comment

Series, symmetrized Normalized Compressed Divergences and their logit transforms

(Major update on 11th January 2019. Minor update on 16th January 2019.) On comparing things The idea of a calculating a distance between series for various purposes has received scholarly attention for quite some time. The most common application is … Continue reading

Posted in Akaike Information Criterion, bridge to somewhere, computation, content-free inference, data science, descriptive statistics, divergence measures, engineering, George Sughihara, information theoretic statistics, likelihood-free, machine learning, mathematics, model comparison, model-free forecasting, multivariate statistics, non-mechanistic modeling, non-parametric statistics, numerical algorithms, statistics, theoretical physics, thermodynamics, time series | 4 Comments

The Johnson-Lindenstrauss Lemma, and the paradoxical power of random linear operators. Part 1.

Updated, 2018-12-04 I’ll be discussing the ramifications of: William B. Johnson and Joram Lindenstrauss, “Extensions of Lipschitz mappings into a Hilbert space, Contemporary Mathematics, 26:189–206, 1984. for several posts here. Some introduction and links to proofs and explications will be … Continue reading

Posted in clustering, data science, dimension reduction, information theoretic statistics, Johnson-Lindenstrauss Lemma, k-NN, Locality Sensitive Hashing, mathematics, maths, multivariate statistics, non-parametric model, numerical algorithms, numerical linear algebra, point pattern analysis, random projections, recommender systems, science, stochastic algorithms, stochastics, subspace projection methods | 1 Comment

Numbers, feelings, and imagination

“But numbers don’t make noises. They don’t have colours. You can’t taste them or touch them. They don’t smell of anything. They don’t have feelings. They don’t make you feel. And they make for pretty boring stories.” That’s from here, … Continue reading

Posted in mathematics, maths, numbers, numerics, oceanography | Leave a comment

Sampling: Rejection, Reservoir, and Slice

An article by Suilou Huang for catatrophe modeler AIR-WorldWide of Boston about rejection sampling in CAT modeling got me thinking about pulling together some notes about sampling algorithms of various kinds. There are, of course, books written about this subject, … Continue reading

Posted in accept-reject methods, American Statistical Association, Bayesian computational methods, catastrophe modeling, data science, diffusion processes, empirical likelihood, Gibbs Sampling, insurance, Markov Chain Monte Carlo, mathematics, Mathematics and Climate Research Network, maths, Monte Carlo Statistical Methods, multivariate statistics, numerical algorithms, numerical analysis, numerical software, numerics, percolation theory, Python 3 programming language, R statistical programming language, Radford Neal, sampling, slice sampling, spatial statistics, statistics, stochastic algorithms, stochastic search | Leave a comment

Fast means, fast moments (originally devised 1984)

(Updated 4th December 2018.) There are many devices available for making numerical calculations fast. Modern datasets and computational problems apply stylized architectures, and use approaches to problems including special algorithms for just calculating dominant eigenvectors or using non-classical statistical mechanisms … Continue reading

Posted in image processing, mathematics, numerical algorithms, numerical software, numerics | 3 Comments

climate model democracy

“One of the most interesting things about the MIP ensembles is that the mean of all the models generally has higher skill than any individual model.” We hold these truths to be self-evident, that all models are created equal, that … Continue reading

Posted in American Association for the Advancement of Science, American Meteorological Association, American Statistical Association, AMETSOC, Anthropocene, attribution, Bayesian model averaging, Bloomberg, citizen science, climate, climate business, climate change, climate data, climate disruption, climate education, climate justice, Climate Lab Book, climate models, coastal communities, coastal investment risks, complex systems, differential equations, disruption, dynamic linear models, dynamical systems, ecology, emergent organization, ensemble methods, ensemble models, ensembles, Eric Rignot, evidence, fear uncertainty and doubt, FEMA, forecasting, free flow of labor, global warming, greenhouse gases, greenwashing, Humans have a lot to answer for, Hyper Anthropocene, Jennifer Francis, Joe Romm, Kevin Anderson, Lévy flights, LBNL, leaving fossil fuels in the ground, liberal climate deniers, mathematics, mathematics education, model-free forecasting, multivariate adaptive regression splines, National Center for Atmospheric Research, obfuscating data, oceanography, open source scientific software, optimization, perceptrons, philosophy of science, phytoplankton | Leave a comment

These are ethical “AI Principles” from Google, but they might as well be `technological principles’

This is entirely adapted from this link, courtesy of Google and Alphabet. Objectives Be socially beneficial. Avoid creating or reinforcing unfair bias. Be built and tested for safety. Be accountable to people. Incorporate privacy design principles. Uphold high standards of … Continue reading

Posted in American Statistical Association, artificial intelligence, basic research, Bayesian, Boston Ethical Society, complex systems, computation, corporate citizenship, corporate responsibility, deep recurrent neural networks, emergent organization, ethical ideals, ethics, extended producer responsibility, friends and colleagues, Google, Google Pixel 2, humanism, investments, machine learning, mathematics, moral leadership, natural philosophy, politics, risk, science, secularism, technology, The Demon Haunted World, the right to know, Unitarian Universalism, UU, UU Humanists | Leave a comment

When linear systems can’t be solved by linear means

Linear systems of equations and their solution form the cornerstone of much Engineering and Science. Linear algebra is a paragon of Mathematics in the sense that its theory is what mathematicians try to emulate when they develop theory for many … Continue reading

Posted in Calculus, dynamic linear models, mathematics, maths, nloptr, numerical algorithms, numerical analysis, numerical linear algebra, numerics, SVD | Leave a comment

The Rule of 135

From SingingBanana.

Posted in Conway's Game of Life, dynamical systems, finite-state machines, mathematical publishing, mathematics, mathematics education, maths, Patterson's Worm, random walks, state-space models, statistical dependence, statistics | Leave a comment

Is the answer to the democratization of Science doing more Citizen Science?

I have been following, with keen interest, the post and comment thread pertaining to “Democratising science” at the blog I monitor daily, … and Then There’s Physics. I think the core subject being discussed is a little different from my … Continue reading

Posted in American Association for the Advancement of Science, American Meteorological Association, American Statistical Association, AMETSOC, astronomy, astrophysics, biology, citizen data, citizen science, citizenship, data science, ecology, education, environment, evidence, life purpose, local self reliance, marine biology, mathematics, mathematics education, maths, moral leadership, new forms of scientific peer review, open source scientific software, science, science education, statistics, the green century, the right to know | Leave a comment

Chesterton’s fence, ecological sensitivity, and the disruption of ecological services

Hat tip to Matt Levine for introducing me to the term Chesteron’s fence: Chesterton’s fence is the principle that reforms should not be made until the reasoning behind the existing state of affairs is understood. … In the matter of … Continue reading

Posted in dynamic generalized linear models, dynamical systems, ecological services, ecology, Ecology Action, mathematics, mathematics education, maths, XKCD | Leave a comment

Happy Newtonmas!

When knowledge conquered fear … And, what better way to celebrate than watching the National Geographic Cosmos episode, When knowledge conquered fear, hosted by the great Dr Neil deGrasse Tyson, Director of the Hayden Planetarium in New York City.

Posted in abstraction, astronomy, astrophysics, atheism, Bill Maher, Bill Nye, Boston Ethical Society, Buckminster Fuller, Carl Sagan, Cosmos, geophysics, Isaac Newton, mathematics, Neill deGrasse Tyson, physics, science, science education, the show | Leave a comment


(Revised and updated Monday, 24th October 2016.) Weapons of Math Destruction, Cathy O’Neil, published by Crown Random House, 2016. This is a thoughtful and very approachable introduction and review to the societal and personal consequences of data mining, data science, … Continue reading

Posted in citizen data, citizen science, citizenship, civilization, compassion, complex systems, criminal justice, Daniel Kahneman, data science, deep recurrent neural networks, destructive economic development, economics, education, engineering, ethics, Google, ignorance, Joseph Schumpeter, life purpose, machine learning, Mathbabe, mathematics, mathematics education, maths, model comparison, model-free forecasting, numerical analysis, numerical software, open data, optimization, organizational failures, planning, politics, prediction, prediction markets, privacy, rationality, reason, reasonableness, risk, silly tech devices, smart data, sociology, Techno Utopias, testing, the value of financial assets, transparency | Leave a comment

Polls, Political Forecasting, and the Plight of Five Thirty Eight

On 17th October 2016 AT 7:30 p.m., Nate Silver of wrote about how, as former Secretary of State Hillary Clinton’s polling numbers got better, it was more difficult for FiveThirtyEight‘s models to justify increasing her probability of winning, although … Continue reading

Posted in abstraction, American Statistical Association, anemic data, citizen science, citizenship, civilization, economics, education, forecasting, information theoretic statistics, mathematics, maths, politics, prediction markets, sociology, the right to know, theoretical physics, thermodynamics | Leave a comment

“All models are wrong. Some models are useful.” — George Box

(Image courtesy of the Damien Garcia.) As a statistician and quant, I’ve thought hard about that oft-cited Boxism. I’m not sure I agree. It’s not that there is such a thing as a perfect model, or correct model, whatever in … Continue reading

Posted in abstraction, American Association for the Advancement of Science, astronomy, astrophysics, mathematics, model-free forecasting, numerics, perceptions, physical materialism, physics, rationality, reason, reasonableness, science, spatial statistics, splines, statistics, the right to know, theoretical physics, time series | Leave a comment

Repaired R code for Markov spatial simulation of hurricane tracks from historical trajectories

(Slight update, 28th June 2020.) I’m currently studying random walk and diffusion processes and their connections with random fields. I’m interested in this because at the core of dynamic linear models, Kalman filters, and state-space methods there is a random … Continue reading

Posted in American Meteorological Association, American Statistical Association, AMETSOC, Arthur Charpentier, atmosphere, diffusion, diffusion processes, dynamic linear models, dynamical systems, environment, geophysics, hurricanes, Kalman filter, Kerry Emanuel, Lévy flights, Lorenz, Markov chain random fields, mathematics, mathematics education, maths, MCMC, mesh models, meteorological models, meteorology, model-free forecasting, Monte Carlo Statistical Methods, numerical analysis, numerical software, oceanography, open data, open source scientific software, physics, random walk processes, random walks, science, spatial statistics, state-space models, statistical dependence, statistics, stochastic algorithms, stochastics, time series | 1 Comment

“Holy crap – an actual book!”

Originally posted on mathbabe:
Yo, everyone! The final version of my book now exists, and I have exactly one copy! Here’s my editor, Amanda Cook, holding it yesterday when we met for beers: Here’s my son holding it: He’s offered…

Posted in American Association for the Advancement of Science, Buckminster Fuller, business, citizen science, citizenship, civilization, complex systems, confirmation bias, data science, data streams, deep recurrent neural networks, denial, economics, education, engineering, ethics, evidence, Internet, investing, life purpose, machine learning, mathematical publishing, mathematics, mathematics education, maths, moral leadership, multivariate statistics, numerical software, numerics, obfuscating data, organizational failures, politics, population biology, prediction, prediction markets, privacy, quantitative biology, quantitative ecology, rationality, reason, reasonableness, rhetoric, risk, Schnabel census, smart data, sociology, statistical dependence, statistics, the right to be and act stupid, the right to know, the value of financial assets, transparency, UU Humanists | Leave a comment

“Stochastic Parameterization: Towards a new view of weather and climate models”

Judith Berner, Ulrich Achatz, Lauriane Batté, Lisa Bengtsson, Alvaro De La Cámara, Hannah M. Christensen, Matteo Colangeli, Danielle R. B. Coleman, Daan Crommelin, Stamen I. Dolaptchiev, Christian L.E. Franzke, Petra Friederichs, Peter Imkeller, Heikki Järvinen, Stephan Juricke, Vassili Kitsios, François … Continue reading

Posted in biology, climate models, complex systems, convergent cross-mapping, data science, dynamical systems, ecology, Ethan Deyle, Floris Takens, George Sughihara, Hao Ye, likelihood-free, Lorenz, mathematics, meteorological models, model-free forecasting, physics, population biology, population dynamics, quantitative biology, quantitative ecology, Scripps Institution of Oceanography, state-space models, statistical dependence, statistics, stochastic algorithms, stochastic search, stochastics, Takens embedding theorem, time series, Victor Brovkin | 4 Comments

France, and Mathematics

Cédric Villani, does Mathematics. “Problems worthy of attack, prove their worth by hitting back.” — Piet Hein

Posted in abstraction, Google, mathematics, mathematics education, maths, networks, Pagerank, percolation theory, point pattern analysis, probability, rationality, reasonableness, stochastic algorithms | Leave a comment